Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domains in the Heisenberg group

We prove geometric $L^p$ versions of Hardy's inequality for the sub-elliptic Laplacian on convex domains $\Omega$ in the Heisenberg group $\mathbb{H}^n$, where convex is meant in the Euclidean sense. When $p=2$ and $\Omega$ is the half-space given by $\langle \xi, \nu\rangle > d$ this generalizes an inequality previously obtained by Luan and Yang. For such $p$ and $\Omega$ the inequality is sharp and takes the form \begin{equation} \int_\Omega |\nabla_{\mathbb{H}^n}u|^2 \, d\xi \geq \frac{1}{4}\int_{\Omega} \sum_{i=1}^n\frac{\langle X_i(\xi), \nu\rangle^2+\langle Y_i(\xi), \nu\rangle^2}{\textrm{dist}(\xi, \partial \Omega)^2}|u|^2\, d\xi, \end{equation} where $\textrm{dist}(\, \cdot\,, \partial \Omega)$ denotes the Euclidean distance from $\partial \Omega$.Comment: 14 page

On the Alexandrov Topology of sub-Lorentzian Manifolds

It is commonly known that in Riemannian and sub-Riemannian Geometry, the metric tensor on a manifold defines a distance function. In Lorentzian Geometry, instead of a distance function it provides causal relations and the Lorentzian time-separation function. Both lead to the definition of the Alexandrov topology, which is linked to the property of strong causality of a space-time. We studied three possible ways to define the Alexandrov topology on sub-Lorentzian manifolds, which usually give different topologies, but agree in the Lorentzian case. We investigated their relationships to each other and the manifold's original topology and their link to causality.Comment: 20 page

Local behavior of p-harmonic Green's functions in metric spaces

We describe the behavior of p-harmonic Green's functions near a singularity in metric measure spaces equipped with a doubling measure and supporting a Poincar\'e inequality

Randomised double-blind trial of megestrol acetate vs placebo in treatment-naive advanced hepatocellular carcinoma

10.1038/bjc.2011.333British Journal of Cancer1057945-952BJCA

Differential distribution of a SINE element in the Entamoeba histolytica and Entamoeba dispar genomes: Role of the LINE-encoded endonuclease

<p>Abstract</p> <p>Background</p> <p><it>Entamoeba histolytica </it>and <it>Entamoeba dispar </it>are closely related protistan parasites but while <it>E. histolytica </it>can be invasive, <it>E. dispar </it>is completely non pathogenic. Transposable elements constitute a significant portion of the genome in these species; there being three families of LINEs and SINEs. These elements can profoundly influence the expression of neighboring genes. Thus their genomic location can have important phenotypic consequences. A genome-wide comparison of the location of these elements in the <it>E. histolytica </it>and <it>E. dispar </it>genomes has not been carried out. It is also not known whether the retrotransposition machinery works similarly in both species. The present study was undertaken to address these issues.</p> <p>Results</p> <p>Here we extracted all genomic occurrences of full-length copies of EhSINE1 in the <it>E. histolytica </it>genome and matched them with the homologous regions in <it>E. dispar</it>, and vice versa, wherever it was possible to establish synteny. We found that only about 20% of syntenic sites were occupied by SINE1 in both species. We checked whether the different genomic location in the two species was due to differences in the activity of the LINE-encoded endonuclease which is required for nicking the target site. We found that the endonucleases of both species were essentially very similar, both in their kinetic properties and in their substrate sequence specificity. Hence the differential distribution of SINEs in these species is not likely to be influenced by the endonuclease. Further we found that the physical properties of the DNA sequences adjoining the insertion sites were similar in both species.</p> <p>Conclusions</p> <p>Our data shows that the basic retrotransposition machinery is conserved in these sibling species. SINEs may indeed have occupied all of the insertion sites in the genome of the common ancestor of <it>E. histolytica </it>and <it>E. dispar </it>but these may have been subsequently lost from some locations. Alternatively, SINE expansion took place after the divergence of the two species. The absence of SINE1 in 80% of syntenic loci could affect the phenotype of the two species, including their pathogenic properties, which needs to be explored.</p

Somatostatin receptor expression, tumour response, and quality of life in patients with advanced hepatocellular carcinoma treated with long-acting octreotide

Octreotide may extend survival in hepatocellular carcinoma (HCC). Forty-one per cent of HCCs have high-affinity somatostatin receptors. We aimed to determine the feasibility, safety, and activity of long-acting octreotide in advanced HCC; to identify the best method for assessing somatostatin receptor expression; to relate receptor expression to clinical outcomes; and to evaluate toxicity. Sixty-three patients with advanced HCC received intramuscular long-acting octreotide 20 mg monthly until progression or toxicity. Median age was 67 years (range 28–81 years), male 81%, Child–Pugh A 83%, and B 17%. The aetiologies of chronic liver disease were alcohol (22%), viral hepatitis (44%), and haemochromatosis (6%). Prior treatments for HCC included surgery (8%), chemotherapy (2%), local ablation (11%), and chemoembolisation (6%). One patient had an objective partial tumour response (2%, 95% CI 0–9%). Serum alpha-fetoprotein levels decreased more than 50% in four (6%). Median survival was 8 months. Thirty four of 61 patients (56%) had receptor expression detected by scintigraphy; no clear relationship with clinical outcomes was identified. There were few grade 3 or 4 toxicities: hyperglycaemia (8%), hypoglycaemia (2%), diarrhoea (5%), and anorexia (2%). Patients reported improvements in some symptoms, but no major changes in quality of life were detected. Long-acting octreotide is safe in advanced HCC. We found little evidence of anticancer activity. A definitive randomised trial would identify whether patients benefit from this treatment in other ways

A cohort study of reproductive and hormonal factors and renal cell cancer risk in women

We examined the association of reproductive and hormonal factors with renal cell cancer risk in a cohort study of 89 835 Canadian women. Compared with nulliparous women, parous women were at increased risk (hazard ratio (HR) 1.78, 95% confidence interval (CI) 1.02–3.09), and there was a significant gradient of risk with increasing levels of parity: relative to nulliparous women, women who had X5 pregnancies lasting 4 months or more had a 2.4-fold risk (HR 1⁄4 2.41, 95% CI 1⁄4 1.27–4.59, P for trend 0.01). Ever use of oral contraceptives was associated with a modest reduction in risk. No associations were observed for age at first live birth or use of hormone replacement therapy. The present study provides evidence that high parity may be associated with increased risk of renal cell cancer, and that oral contraceptive use may be associated with reduced risk

Reproducibility of microarray data: a further analysis of microarray quality control (MAQC) data

<p>Abstract</p> <p>Background</p> <p>Many researchers are concerned with the comparability and reliability of microarray gene expression data. Recent completion of the MicroArray Quality Control (MAQC) project provides a unique opportunity to assess reproducibility across multiple sites and the comparability across multiple platforms. The MAQC analysis presented for the conclusion of inter- and intra-platform comparability/reproducibility of microarray gene expression measurements is inadequate. We evaluate the reproducibility/comparability of the MAQC data for 12901 common genes in four titration samples generated from five high-density one-color microarray platforms and the TaqMan technology. We discuss some of the problems with the use of correlation coefficient as metric to evaluate the inter- and intra-platform reproducibility and the percent of overlapping genes (POG) as a measure for evaluation of a gene selection procedure by MAQC.</p> <p>Results</p> <p>A total of 293 arrays were used in the intra- and inter-platform analysis. A hierarchical cluster analysis shows distinct differences in the measured intensities among the five platforms. A number of genes show a small fold-change in one platform and a large fold-change in another platform, even though the correlations between platforms are high. An analysis of variance shows thirty percent of gene expressions of the samples show inconsistent patterns across the five platforms. We illustrated that POG does not reflect the accuracy of a selected gene list. A non-overlapping gene can be truly differentially expressed with a stringent cut, and an overlapping gene can be non-differentially expressed with non-stringent cutoff. In addition, POG is an unusable selection criterion. POG can increase or decrease irregularly as cutoff changes; there is no criterion to determine a cutoff so that POG is optimized.</p> <p>Conclusion</p> <p>Using various statistical methods we demonstrate that there are differences in the intensities measured by different platforms and different sites within platform. Within each platform, the patterns of expression are generally consistent, but there is site-by-site variability. Evaluation of data analysis methods for use in regulatory decision should take no treatment effect into consideration, when there is no treatment effect, "a fold-change cutoff with a non-stringent p-value cutoff" could result in 100% false positive error selection.</p

Methods for selecting the best evidence to inform a NICE technology appraisal on selective internal radiation therapies for hepatocellular carcinoma

Background: Systematic reviews of medical devices are particularly challenging as the quality of evidence tends to be more limited than evidence on pharmaceutical products. This article describes the methods used to identify, select and critically appraise the best available evidence on selective internal radiation therapy devices for treating hepatocellular carcinoma, to inform a technology appraisal for the National Institute for Health and Care Excellence. Methods: A comprehensive search of ten medical databases and six grey literature sources was undertaken to identify studies of three devices (TheraSphere®, SIR-Spheres® and QuiremSpheres®) for treating hepatocellular carcinoma. The large evidence base was scoped before deciding what level of evidence to include for data extraction and critical appraisal. The methodological quality of the included studies was assessed using criteria relevant to each study design. Results: Electronic searches identified 4755 records; over 1000 met eligibility criteria after screening titles and abstracts. A hierarchical process was used to scope these records, prioritising comparative studies over non-comparative studies, where available. 194 full papers were ordered; 64 met the eligibility criteria. For each intervention, studies were prioritised by study design and applicability to current UK practice, resulting in 20 studies subjected to critical appraisal and data extraction. Only two trials had a low overall risk of bias. In view of the poor quality of the research evidence, our technology appraisal focused on the two higher quality trials, including a thorough critique of their reliability and generalisability to current UK practice. The 18 poorer quality studies were briefly summarised; many were very small and results were often contradictory. No definitive conclusions could be drawn from the poorer quality research evidence available. Conclusions: A systematic, pragmatic process was used to select and critically appraise the vast quantity of research evidence available in order to present the most reliable evidence on which to develop recommendations

Tamoxifen is not effective in good prognosis patients with hepatocellular carcinoma

BACKGROUND: Large randomised clinical trials and systematic reviews substantiate that tamoxifen is ineffective in improving survival of patients with hepatocellular carcinoma (HCC). However, a recent report suggested that the drug might prolong survival among patients with well preserved liver function. The aim of this paper is to validate this hypothesis. METHODS: We used the updated database of the phase 3 randomised CLIP-1 trial that compared tamoxifen with supportive therapy. Primary endpoint was overall survival. Treatment arms were compared within strata defined according to the Okuda stage and the CLIP-score. Survival differences were tested by the Log-rank test. RESULTS: Tamoxifen was not effective in prolonging survival in Okuda I-II subgroup (p = 0.501). Median survival times were equal to 16.8 (95%CI 12.7–18.5) months for tamoxifen and 16.8 (95%CI 13.5–22.4) months for the control arms; 1-year survival probabilities were equal to 58.8% (95%CI 51.7–65.8) and 59.4 (95%CI 52.5–66.2), respectively. Similar results were observed in the better CLIP subgroup (score 0/1), without evidence of difference between the two treatment arms (p = 0.734). Median survival times were equal to 29.2 (95%CI 20.1–36.4) months with tamoxifen and 29.0 (95%CI 23.3–35.2) months without; 1-year survival probabilities were equal to 80.9% (95%CI 72.5–89.3) with tamoxifen and 77.1% (95%CI 68.6–85.7) for the control arm. CONCLUSION: The recent suggestion that tamoxifen might be effective in the subgroup of patients with better prognosis is not supported by a reanalysis of the CLIP-1 trial. Tamoxifen should no longer be considered for the treatment of HCC patients and future trials of medical treatment should concentrate on different drugs